Time: July 5-July 6

Venue: Lecture Hall

Abstract: Shtukas were introduced first by Drinfeld in the function fields case to establish Langlands correspondences. The p-adic analogue is found much later by Peter Scholze. One of the main difficulties in the p-adic case is that it is not a classical algebraic or analytic geometry object, rather it lives in the new p-adic geometry developed by Scholze. Striking applications to the local Langlands program have been worked out by Fargues-Scholze. In the two talks, I will introduce a global application of these ideas, namely how it helps to settle the Eichler-Shimura relation for Shimura varieties.